Question

Find the vertices and foci of the hyperbola with equation quantity x minus five squared divided by eighty one minus the quantity of y minus one squared divided by one hundred and forty four = 1

Answer 1

@saseal

Answer 2

waddup?

Answer 3

\[\frac{(x-5)^2}{81}-\frac{(y-1)^2}{4}=1\]?

Answer 4

this is way easier than you think
but you need to know two things first
a) the center and
b) which way it is oriented

Answer 5

I know that the hyperbolas are oriented left/right

Answer 6

i thought ya all that earlier

Answer 7

taught*

Answer 8

center?

Answer 9

@satellite73 you mean what i taught him?

Answer 10

(0,5) ?

Answer 11

My bad, (5, 1)

Answer 12

yes

Answer 13

Ok so now what can I do?

Answer 14

find c

Answer 15

\[\frac{(x-5)^2}{81}-\frac{(y-1)^2}{4}=1\]\[\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\]
what is \(a\)?

Answer 16

Ok. c = 15

Answer 17

a = 81, b =144

Answer 18

no

Answer 19

no

Answer 20

\[a^2=81,b^2=144\]

Answer 21

\[c^2=a^2+b^2\]

Answer 22

thats why i told ya to put em into ^2 form

Answer 23

Oh sorry. a = 9, b = 12

Answer 24

Ok, so c = 15 because c^2 = 225

Answer 25

@saseal

Answer 26

yea?

Answer 27

you know the hyperbola is transverse in x-axis so ( center +/- c, center) is your foci

Answer 28

and same for the vertices

Answer 29

Wait. These are my choices:

A. Vertices: (17, 1), (-7, 1); Foci: (-7, 1), (17, 1)
B. Vertices: (14, 1), (-4, 1); Foci: (-10, 1), (20, 1)
C. Vertices: (1, 14), (1, -4); Foci: (1, -10), (1, 20)
D. Vertices: (1, 17), (1, -7); Foci: (1, -7), (1, 17)

So I know it has to be between A and B.

Answer 30

Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7).

If my answer choices are:
A. y squared over nine minus x squared over forty = 1
B. y squared over forty minus x squared over nine = 1
C. y squared over forty nine minus x squared over nine = 1
D. y squared over nine minus x squared over forty nine = 1

I was thinking it was between B and D.

Answer 31

lemme check

Answer 32

you see foci is c^2 = a^2+b^2
so we get 7^2 - 3^2 = 40

Answer 33

Oh ok. So that would make it A.